Transcript Using GEMINI to study multiplicity distributions of light charged particles and neutrons Adil Bahalim Davidson College Dr.

Using GEMINI to study multiplicity distributions of light
charged particles and neutrons
Adil Bahalim
Davidson College
Dr. Joseph Natowitz (Advisor), Dr. Seweryn Kowalski (Mentor)
Summer REU 2005 – TAMU Cyclotron Institute
Background
Heavy Ion Collisions
Reconstruction




Figure 1. Immediately after the collision, the system undergoes a
multifragmentation process. Primary fragments emerge from the projectile and
target nuclei. These fragments separate and de-excite during secondary
emission, decaying to secondary fragments while giving off light charged
particles and neutrons.
AMD Model Reconstruction
Main hurdle is secondary decay
(intermediate mass fragments) which
makes it difficult to reconstruct primary
fragments
Antisymmetrized Molecular Dynamics
(AMD) calculations used have shown to
be good models for reconstruction
Mean multiplicities (obtained from
experiment) and distributions widths
(difficult to obtain) of LP’s are used as
input parameters in GEMINI
GEMINI is a statistical modeling code that
uses the Monte-Carlo method to simulate
sequential binary decays of nuclei
Figure 2. In this previous study, AMD Model calculations were used
to reconstruct simulated decays of several IMF’s. The filled stars
represent the original parent nuclei. The open stars show the
reconstructed parent nuclei. There is a good fit between the two,
making this a reasonable model for reconstruction.
Procedure
GEMINI Simulations
Simulation Data
Distribution Widths vs. Mean Multiplicities
Neutron Width vs. Mean Multiplicity Z=3 to Z=40
Simulated 1000 decay events for
each nucleus from Z=3 to Z=40 with
at least one from each:
 Stability line (i.e. ~ Z = N)
 Proton-rich side (~ Z > N)
 Neutron-rich side (N > Z)
Excitation energies ranged from 2 to 5
MeV/amu in .5 MeV/amu increments
Assumed constant inverse level
density parameter (8)

1.6
1.6
1.4
1.4
1.2
1.2
1
1
1.2
Width
Width
Width
1
0.8
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.6
0.4
0.2
0
0
0
0
2
4
6
8
10
12
14
16
0
18
1
2
3
4
5
6
7
0
8
0.5
1
1.5
Mean Multiplicity
Triton Width vs. Mean Multiplicity Z=3 to Z=40
3Helium Width vs. Mean Multiplicity Z=3 to Z=40
1
2
2.5
Mean Multiplicity
Mean Multiplicity
4Helium Width vs. Mean Multiplicity Z=3 to Z=40
2
0.7
1.8
0.9
0.6
1.6
0.8
0.5
0.7
1.4
1.2
0.6
Width
0.4
Width

1.6
1.4
Width

Deuteron Width vs. Mean Multiplicity Z=3 to Z=40
Proton Width vs. Mean Multiplicity Z=3 to Z=40
1.8
0.5
1
0.3
0.8
0.4
0.3
0.6
0.2
0.4
0.2
0.1
0.2
0.1
0
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
0
0.05
0.1
0.15
0.2
0.25
0.3
Mean Multiplicity
Mean Multiplicity
0.35
0.4
0.45
0.5
0
0.5
1
1.5
2
2.5
Mean Multiplicity
Figure 4. Global plots of all series from Z=3 to Z=40 with excitation energies from 2.5 MeV/amu to 5 MeV/amu
for each of the light particles emitted. Though on different scales, all plots show a positive trend as the mean
multiplicities of the particles increase. 4He has a greater spread than the rest of the particles. A possible cause is
the limitation of the computer code.
Figure 3. A typical sample of data gathered by GEMINI of each of
the light particles emitted during decay. These data were collected
for the decay of the 95Zr.
Results
Best Fit Function at Exc.
Energy = 3 MeV/amu
Neutron Width vs. Mean Multiplicity at Exc Energy = 3 MeV/amu
Proton Width vs. Mean Multiplicity at Exc Energy = 3 MeV/amu
Deuteron Width vs. Mean Multiplicity at Exc Energy = 3 MeV/amu
1.4
1.6
1.4
Conclusion
Neutron Power-Function
Parameters A & B (y=AxB)

Proton Power Function Parameter B vs. EE
Proton Power Function Parameter A vs. EE
1.2
1.2
1
1.2
0.8
0.7
0.8
Width
y = 0.6859x0.3549
R2 = 0.9192
Width
Width
0.8
0.6
y = 0.9245x0.5224
R2 = 0.9778
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
0
0
2
4
6
8
10
12
0
14
0
0
1
2
Mean Multiplicity
3
4
5
6
0
0.2
0.4
0.6
Mean Multiplicity
Triton Width vs. Mean Multiplicity at Exc Energy = 3 MeV/amu
1
1.2
Mean Multiplicity
4Helium Width vs. Mean Multiplicity at Exc Energy = 3 MeV/amu
3Helium Width vs. Mean Multiplicity at Exc Energy = 3 MeV/amu
0.7
0.8
0.5
1.2
0.4
0.3
Width
Width
Width
y = 0.9534x
R2 = 0.9989
1
y = 0.9185x0.4813
R2 = 0.9976
0.3
y = 0.016x + 0.6331
2
R = 0.7808
0
0.5
0.4914
0.5
0.4
0.3
0.2
0
1.4
0.6
0.4
0.6
0.1
1.6
0.6
Parameter A
0.8
y = 0.6065x0.3583
R2 = 0.9766
Parameter A
1
1
y = 0.9637x0.5068
R2 = 0.7343
0.8
1
2
3
Excitation Energy
4
5
6
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
y = 0.014x + 0.3183

2
R = 0.8711
0
1
2
3
4
5
6
Excitation Energy
0.6
0.2
0.2
0.4
Figure 6. The graph on the right shows the values of the power-function fit parameter A at each of the
excitation energies. The graph on the left shows the values for B. There is an almost linear trend for
each parameter.
0.1
0.1
0.2
0
0
0
0.05
0.1
0.15
0.2
Mean Multiplicity
0.25
0.3
0.35
0.4
0
0
0.05
0.1
0.15
0.2
Mean Multiplicity
0.25
0.3
0.35
0
0.5
1
1.5
2
Mean Multiplicity
Figure 5. Width vs. Mean Multiplicity plots for each light particle for all nuclei simulations at an excitation
energy of 3 MeV/amu. Power functions had the best fits to these plots. All fits, excluding 4He, have a
correlation coefficient, R2, of greater than .90.
2.5
As expected, we found the
relation between the mean
multiplicities and distribution
widths of the LCP’s and neutrons
These relations can be used as
references to determine the
distribution widths from the
experimental data on mean
multiplicities and implement them
as input parameters for the
reconstruction models